After suffering a historic home whitewash against New Zealand, India flew out on Monday to prepare for the upcoming Border-Gavaskar trophy.
Sharma was not on the plane, with the Indian skipper expected to miss at least the first Test against Australia in Perth due to personal reasons.
Gambhir offered no update on Sharma's availability but confirmed fast bowler Jasprit Bumrah would captain India should the veteran opener be unavailable.
Sharma and Kohli both averaged just 15 across three losing Tests against New Zealand as the Black Caps became the first touring team to win a red-ball series in India for 12 years.
Ricky Ponting says out-of-form Rohit Sharma and Virat Kohli are lucky to be playing internationally. (Dean Lewins/AAP PHOTOS)
Those performances led to Ponting, a long-time coach in the Indian Premier League, questioning their form.
"There wouldn't be anyone else probably even playing international cricket as a top-order batsman that's only scored two Test match hundreds in five years," Ponting said on an ICC podcast.
Gambhir was quick to bite back at those comments when quizzed before the Indian team left Mumbai.
"What does Ponting have to do with Indian cricket? I think he should think about Australian cricket," he said.
"More importantly, I have got no concerns whatsoever for Virat and Rohit.
"They are incredibly tough men.
"They've achieved a lot for Indian cricket, and they will continue to achieve a lot in the future as well.
"For me, the most important thing is that they still work really hard, and they're still passionate, they still want to achieve a lot more.
"The hunger in that dressing room is incredibly important for me.
"I feel there's a lot of hunger, especially after what has happened in the last series."
Veteran KL Rahul and Abhimanyu Easwaran, who has played more than 100 first-class matches without a Test debut, are in line to take Sharma's spot should he not play.
The pair were out cheaply in both innings against Australia A at the MCG last week.
Rahul's second-innings dismissal, where he tried to leave the ball before getting bowled, would have been concerning for India.
Rahul was batting in the middle-order for India before he was dropped for the third Test against New Zealand, but most of his international runs have come when opening the batting.
"That is the quality of the man, that he can actually bat at the top of the order, he can bat at No.3 and he can actually bat at No.6 as well," Gambhir said of Rahul.
"You need quite a lot of talent to be doing these kind of jobs.
"Imagine how many countries have players like KL who can open the batting and can bat at No.6 as well.
"I feel that he can do the job for us, especially if Rohit is not available for the first Test."
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